Cho log b (a + 1) > 0, khi đó khẳng định nào sau đây là đúng? (b - 1) a > 0

* Hướng dẫn giải

Đáp án A.

Phương pháp

$$\begin{gathered} {\log }_{a}f\left(x\right)>{\log }_{a}g\left(x\right) \\ \iff \left[\begin{array}{l}\left\{\begin{array}{l}a>1\\ f\left(x\right)>g\left(x\right)\end{array}\right.\\ \left\{\begin{array}{l}0<a<1\\ f\left(x\right)<g\left(x\right)\end{array}\right.\end{array}\right. \end{gathered}$$

Cách giải

ĐK: $0<b\ne 1;a>-1$

$$\begin{gathered} {\log }_{a}f\left(x\right)>{\log }_{a}g\left(x\right) \\ \iff \left[\begin{array}{l}\left\{\begin{array}{l}b>1\\ a+1>1\end{array}\right.\\ \left\{\begin{array}{l}0<b<1\\ a+1<1\end{array}\right.\end{array}\right. \\ \iff \left[\begin{array}{l}\left\{\begin{array}{l}b>1\\ a>0\end{array}\right.\\ \left\{\begin{array}{l}0<b<1\\ a<0\end{array}\right.\end{array}\right. \\ \iff \left[\begin{array}{l}\left\{\begin{array}{l}b-1>0\\ a>0\end{array}\right.\\ \left\{\begin{array}{l}b-1<0\\ a<0\end{array}\right.\end{array}\right.\Rightarrow a\left(b-1\right)>0 \end{gathered}$$